Partial sum of 1-x

On WolframAlpha I see that the sum of x+1 is given by

But if I want to start at i=1 this sum is no longer valid!! Was a surprise at first but i see now it makes sense, but then what is the way to adjust these partial sum formulas for starting at different numbers, or do I have to think of a totally new formula when i want to do something like this?

But if I want to start at i=1 this sum is no longer valid!! Was a surprise at first but i see now it makes sense, but then what is the way to adjust these partial sum formulas for starting at different numbers, or do I have to think of a totally new formula when i want to do something like this?

Thank you

First something is weird with your indexes. You are summing over i but there are know i's in your formula!

I assume you mean something like this

Expand the sum out to get

The sum or squares and the sum or the first n integers are known formula's